深度学习 —— 个人学习笔记6（权重衰减）

声明

本文章为个人学习使用，版面观感若有不适请谅解，文中知识仅代表个人观点，若出现错误，欢迎各位批评指正。

十三、权重衰减

使用以下公式为例做演示：

$\sum_{i=1}^{d} 0.01x_i + \varepsilon \quad where \quad \varepsilon \; ～ \; N ( 0 , 0.01^2 )$

权重衰减的实现

import torch
from torch import nn
from d2l import torch as d2l
from IPython import displaydef synthetic_data(w, b, num_examples):"""生成 y = Xw + b + 噪声。"""X = torch.normal(0, 1, (num_examples, len(w))).cuda()                    # 均值为 0，方差为 1，有 num_examples 个样本，列数为 w 长度y = torch.matmul(X, w).cuda() + b                                        # y = Xw + by += torch.normal(0, 0.01, y.shape).cuda()                               # 随机噪音return X, y.reshape((-1, 1))                                             # x，y作为列向量返回class Animator:                                                                   # 定义一个在动画中绘制数据的实用程序类 Animator"""在动画中绘制数据"""def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,ylim=None, xscale='linear', yscale='linear',fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,figsize=(3.5, 2.5)):# 增量地绘制多条线if legend is None:legend = []d2l.use_svg_display()self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)if nrows * ncols == 1:self.axes = [self.axes, ]# 使用lambda函数捕获参数self.config_axes = lambda: d2l.set_axes(self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)self.X, self.Y, self.fmts = None, None, fmtsdef add(self, x, y):# Add multiple data points into the figureif not hasattr(y, "__len__"):y = [y]n = len(y)if not hasattr(x, "__len__"):x = [x] * nif not self.X:self.X = [[] for _ in range(n)]if not self.Y:self.Y = [[] for _ in range(n)]for i, (a, b) in enumerate(zip(x, y)):if a is not None and b is not None:self.X[i].append(a)self.Y[i].append(b)self.axes[0].cla()for x, y, fmt in zip(self.X, self.Y, self.fmts):self.axes[0].plot(x, y, fmt)self.config_axes()display.display(self.fig)# 通过以下两行代码实现了在PyCharm中显示动图d2l.plt.draw()d2l.plt.pause(interval=0.001)display.clear_output(wait=True)d2l.plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']n_train, n_test, num_inputs, batch_size = 20, 100, 200, 5
true_w, true_b = torch.ones((num_inputs, 1)).cuda() * 0.01, 0.05
train_data = synthetic_data(true_w, true_b, n_train)
train_iter = d2l.load_array(train_data, batch_size)
test_data = synthetic_data(true_w, true_b, n_test)
test_iter = d2l.load_array(test_data, batch_size, is_train=False)##############    权重衰减的实现    #############
def init_params():""" 初始化参数 """w = torch.normal(0, 1, size=(num_inputs, 1)).cuda()b = torch.zeros(1).cuda()w.requires_grad_(True)b.requires_grad_(True)return [w, b]def l2_penalty(w):""" 定义 L2 范数惩罚 """return (torch.sum(w.pow(2)) / 2).cuda()def train(lambd):flag_button = "使用"w, b = init_params()net, loss = lambda X: d2l.linreg(X, w, b), d2l.squared_lossnum_epochs, lr = 150, 0.005animator = Animator(xlabel='epochs', ylabel='loss', yscale='log',xlim=[5, num_epochs], legend=['train', 'test'])for epoch in range(num_epochs):for X, y in train_iter:# 增加了 L2 范数惩罚项，、# 广播机制使 l2_penalty(w) 成为一个长度为 batch_size 的向量l = loss(net(X), y) + lambd * l2_penalty(w)l.sum().backward()d2l.sgd([w, b], lr, batch_size)if (epoch + 1) % 5 == 0:animator.add(epoch + 1, (d2l.evaluate_loss(net, train_iter, loss),d2l.evaluate_loss(net, test_iter, loss)))# print('w的L2范数是：', torch.norm(w).item())if lambd == 0:flag_button = "禁用"d2l.plt.title(f"{flag_button}权重衰减 (lambda = {lambd})\nw 的 L2 范数是：{torch.norm(w).item()}")d2l.plt.show()train(lambd=0)train(lambd=15)

权重衰减的简洁实现

import torch
from torch import nn
from d2l import torch as d2l
from IPython import displaydef synthetic_data(w, b, num_examples):"""生成 y = Xw + b + 噪声。"""X = torch.normal(0, 1, (num_examples, len(w))).cuda()                    # 均值为 0，方差为 1，有 num_examples 个样本，列数为 w 长度y = torch.matmul(X, w).cuda() + b                                        # y = Xw + by += torch.normal(0, 0.01, y.shape).cuda()                               # 随机噪音return X, y.reshape((-1, 1))                                             # x，y作为列向量返回class Animator:                                                                   # 定义一个在动画中绘制数据的实用程序类 Animator"""在动画中绘制数据"""def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,ylim=None, xscale='linear', yscale='linear',fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,figsize=(3.5, 2.5)):# 增量地绘制多条线if legend is None:legend = []d2l.use_svg_display()self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)if nrows * ncols == 1:self.axes = [self.axes, ]# 使用lambda函数捕获参数self.config_axes = lambda: d2l.set_axes(self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)self.X, self.Y, self.fmts = None, None, fmtsdef add(self, x, y):# Add multiple data points into the figureif not hasattr(y, "__len__"):y = [y]n = len(y)if not hasattr(x, "__len__"):x = [x] * nif not self.X:self.X = [[] for _ in range(n)]if not self.Y:self.Y = [[] for _ in range(n)]for i, (a, b) in enumerate(zip(x, y)):if a is not None and b is not None:self.X[i].append(a)self.Y[i].append(b)self.axes[0].cla()for x, y, fmt in zip(self.X, self.Y, self.fmts):self.axes[0].plot(x, y, fmt)self.config_axes()display.display(self.fig)# 通过以下两行代码实现了在PyCharm中显示动图d2l.plt.draw()d2l.plt.pause(interval=0.001)display.clear_output(wait=True)d2l.plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']n_train, n_test, num_inputs, batch_size = 20, 100, 200, 5
true_w, true_b = torch.ones((num_inputs, 1)).cuda() * 0.01, 0.05
train_data = synthetic_data(true_w, true_b, n_train)
train_iter = d2l.load_array(train_data, batch_size)
test_data = synthetic_data(true_w, true_b, n_test)
test_iter = d2l.load_array(test_data, batch_size, is_train=False)##############    权重衰减的简洁实现    #############def train_concise(wd):flag_button = "使用"net = nn.Sequential(nn.Linear(num_inputs, 1)).cuda()for param in net.parameters():param.data.normal_().cuda()loss = nn.MSELoss(reduction='none').cuda()num_epochs, lr = 150, 0.005# 偏置参数没有衰减trainer = torch.optim.SGD([{"params":net[0].weight,'weight_decay': wd},{"params":net[0].bias}], lr=lr)animator = Animator(xlabel='epochs', ylabel='loss', yscale='log',xlim=[5, num_epochs], legend=['train', 'test'])for epoch in range(num_epochs):for X, y in train_iter:trainer.zero_grad()l = loss(net(X), y)l.mean().backward()trainer.step()if (epoch + 1) % 5 == 0:animator.add(epoch + 1,(d2l.evaluate_loss(net, train_iter, loss),d2l.evaluate_loss(net, test_iter, loss)))# print('w的L2范数：', net[0].weight.norm().item())if wd == 0:flag_button = "禁用"d2l.plt.title(f"{flag_button}权重衰减 (lambda = {wd})\nw 的 L2 范数是：{net[0].weight.norm().item()}")d2l.plt.show()train_concise(0)train_concise(-2)